What is the downward acceleration?

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The discussion focuses on calculating the downward acceleration of a yo-yo, which is modeled as a uniform disk unwinding from a fixed string. Participants apply Newton's second law to both translational and rotational motion, leading to the derived formula for acceleration, ac = g/(1 + R^2/2r^2). The conversation also touches on the complexities of analyzing a slipping cylinder on a ramp, specifically how to incorporate kinetic friction into the calculations. The frictional force is identified as μN, which needs to be included in the equations for accurate results. Overall, the thread emphasizes the importance of considering both forces and torques in these dynamics problems.
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A yoyo consists of aunfirom disk with a string wound around the rim. the upper end of the string is held fixed. the yoyo unwinds as it drops. what is the downward acceleration?

I got the idea that Inertia*acceleration=force on the rim.
 
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Consider the forces acting on the disk and the torques they produce. Apply Newton's 2nd law to both translational and rotational motion.
 
I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?
 
deanwudean said:
I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)
If the yo-yo is just a uniform disk with the string wound around the rim, this answer can be simplified.

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?
Just add the friction force to the mix. It equals \mu N.
 
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